As he lay dying, the Pharaoh proclaimed: "I bequeath 1/3 of my estate to
my oldest child; 1/4 of my estate to the next oldest child; and to each
succeeding child, except the youngest, the next unit fraction of my
estate; and to the youngest the remainder."

I pick 5 digits, and write them down. My friend tells me a sum. Then I
pick 5 more digits, he picks 5, I pick 5, and he picks 5. The sum he told
me is the sum of all 5 lines. How did he know what it would be?

I have to find a 10 digit number which uses each of the digits 0-9
such that the first digit is divisible by 1, the first two digits make
a number divisible by 2, the first three digits make a number
divisible by 3, and so on up to all ten digits making a number
divisible by 10. I figured it out using mostly guess and check, but
it took a long time. Is there a quicker way?

A teacher puts one hat on each of three students' heads and then
discards the remaining two hats so they cannot be seen. Then the first
child is told he can look at the other two children and from the color
of their hats, he can guess what color he is wearing...

I have a machine that only types out ones (no spaces or tricks
involved). What procedure must you do to this machine to get any given
finite set? For example [2,85,11,5,60]. For a different set, the
number of ones that the machine types out will vary.

A building has 7 elevators, each stopping on at most 6 floors. If you
take the right elevator you can get to any floor from any other floor
without changing elevators. What is the greatest number of floors the
building can have?

A Volunteer writes different numbers from 1 to 125 on six cards, and
keeps one. The Host arranges the others in some order and gives them to
the Partner, who then says the number on the missing card. How?

A snail is climbing a window-pane, beginning in the evening at a
height of e minus 1 meter from the base. It loses 1 meter each night.
On the second day, it doubles its altitude of the morning. On the
third day, it triples the altitude of the morning, and so on. What
will be its altitude on the 51st day at dawn?